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Graph the following inequalities:
a. y > x² + 1
b. x² + y² ≥ 4
Solution:
a. For y > x² + 1, the given equation is a parabola that concave upward whose vertex is V(0, -1). Since the sign of inequality is greater than, then all points along the curve are not included in the solution. If x = 0 and y = 0, then the given equation reduces to 0 > 1 which is not correct and that point is not included in the solution. Therefore, the graph of the given equation is
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| Photo by Math Principles in Everyday Life |
b. For x² + y² ≥ 4, the given equation is a circle whose center is C(0, 0) and its radius is r = 2. Since the sign of inequality is greater than or equal to, then all points along the curve are included in the solution. If x = 0 and y = 0, then the given equation reduces to 0 ≥ 4 which is not correct and that point is not included in the solution. Therefore, the graph of the given equation is
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| Photo by Math Principles in Everyday Life |